Subgroups — #22586474

Order 9088.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇₁⋊C₃₂	C₂	1	2	yes	maximal
2	C₄×C₁₆×C₇₁	C₂	1	1	yes	maximal, characteristic
3	C₇₁⋊C₃₂	C₄	1	4	yes	complemented
4	C₂×C₁₆×C₇₁	C₄	1	1	yes	characteristic
5	C₂×C₁₆×C₇₁	C₂²	1	1	yes	characteristic
6	C₄×C₈×C₇₁	C₄	1	1	yes	characteristic
7	C₂×C₈×C₇₁	C₈	1	1	yes	characteristic
8	C₂×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
9	C₄²×C₇₁	C₈	1	1	yes	characteristic
10	C₁₆×C₇₁	C₈	1	2	yes	—
11	C₁₆×C₇₁	C₂×C₄	1	2	yes	—
12	C₂×C₄×C₇₁	C₁₆	1	2	yes	—
13	C₂×C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
14	C₈×C₇₁	C₁₆	1	2	yes	—
15	C₈×C₇₁	C₄²	1	1	yes	characteristic
16	C₈×C₇₁	C₂×C₈	1	1	yes	characteristic
17	C₂²×C₇₁	C₂×C₁₆	1	1	yes	characteristic
18	C₄×C₇₁	—	2	2	no	—
19	C₄×C₇₁	C₄×C₈	1	1	yes	characteristic
20	C₄×C₇₁	C₂×C₁₆	1	1	yes	characteristic
21	C₂×C₇₁	C₄×C₁₆	1	1	yes	characteristic
22	C₂×C₇₁	M₆₄	1	2	yes	—
23	#1397	—	71	1	no	maximal, Sylow
24	C₇₁	#1397	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₃₂	—	71	2	no	—
26	C₄×C₁₆	D₇₁	1	1	yes	characteristic
27	C₂×C₁₆	Dic₇₁	1	1	yes	characteristic
28	C₂×C₁₆	C₂×D₇₁	1	1	yes	characteristic
29	C₄×C₈	Dic₇₁	1	1	yes	characteristic
30	C₃₂	—	71	4	no	—
31	C₂×C₈	C₇₁⋊C₈	1	1	yes	characteristic
32	C₂×C₈	C₂×Dic₇₁	1	1	yes	characteristic
33	C₄²	C₇₁⋊C₈	1	1	yes	characteristic
34	C₁₆	C₇₁⋊C₈	1	2	yes	—
35	C₁₆	C₄×D₇₁	1	2	yes	—
36	C₂×C₄	C₇₁⋊C₁₆	1	2	yes	—
37	C₂×C₄	C₂×C₇₁⋊C₈	1	1	yes	characteristic
38	C₈	C₇₁⋊C₁₆	1	2	yes	—
39	C₈	C₄×Dic₇₁	1	1	yes	characteristic
40	C₈	C₂×C₇₁⋊C₈	1	1	yes	characteristic
41	C₂²	C₂×C₇₁⋊C₁₆	1	1	yes	characteristic
42	C₄	—	2	2	no	—
43	C₄	C₄×C₇₁⋊C₈	1	1	yes	characteristic
44	C₄	C₂×C₇₁⋊C₁₆	1	1	yes	characteristic
45	C₂	C₄×C₇₁⋊C₁₆	1	1	yes	characteristic
46	C₂	#17985833	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₁₆	C₂×D₇₁
commutator	C₂×C₇₁	C₄×C₁₆
Fitting	C₄×C₁₆×C₇₁	C₂
socle	C₂²×C₇₁	C₂×C₁₆
hypercenter	C₄×C₁₆	D₇₁
hypocenter	C₇₁	#1397
LCS	G ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₁₆ ◁ C₄×C₁₆

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. C₇₁⋊C₃₂	C₄	semidirect
24. C₇₁	#1397	semidirect